Not calculated when using Subs function

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Deokjae Jeong
Deokjae Jeong 2016-9-15
评论： Deokjae Jeong 2016-9-17
When using Subs function,the output of v is (14*2^(2/5)*3^(3/5)*15^(3/5)*25^(2/5))/75, which is 8.7615770046893.
Why the output is not simply 8.761577004689 ?
syms px py w v a
v=(w*(a/px)^a*((1-a)/py)^(1-a))
a=0.4
px=3
py=5
w=70
v=subs(v)

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回答（2 个）

John D'Errico
John D'Errico 2016-9-15
Because that is not the exact number.
simplify(v)
ans =
(14*3^(1/5)*10^(2/5))/5
I'm sure you can see that as soon as you decide to write it in decimal form, no matter what, you cannot write it exactly. And since this is the symbolic TB you are talking about, what do you expect?
vpa(v)
ans =
8.7615770046893145084508459712354
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John D'Errico
John D'Errico 2016-9-16
vpa will give you a decimal (but still in symbolic form) approximation to the number, yes. So will double, with fewer digits as a double precision number.

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Walter Roberson
Walter Roberson 2016-9-15
(14*2^(2/5)*3^(3/5)*15^(3/5)*25^(2/5))/75 is not 8.7615770046893 . The expression is only approximately 8.7615770046893 . A better approximation would be 8.761577004689314508450845971235390274526747228228561126229132624459900445322460260513472705827961752 and it can be shown that the result is irrational (and thus non-terminating). Another way of writing the expression is (14/75)*50^(2/5)*45^(3/5) which you can see involves fifth roots.
The purpose of the symbolic toolbox is to calculate exact solutions whenever possible. The decimal value you list is not an exact solution, only a decimal approximation of it.
If you want the decimal approximation, use vpa() or double()

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